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A083348 Numbers k such that r(k) = Sum(e/p: k = Product(p^e)) > 1.

%I A083348 #39 Feb 23 2024 07:27:28
%S A083348 8,12,16,18,20,24,28,30,32,36,40,44,48,52,54,56,60,64,68,72,76,80,81,
%T A083348 84,88,90,92,96,100,104,108,112,116,120,124,126,128,132,135,136,140,
%U A083348 144,148,150,152,156,160,162,164,168,172,176,180,184,188,189,192,196,198
%N A083348 Numbers k such that r(k) = Sum(e/p: k = Product(p^e)) > 1.
%C A083348 The number of terms not exceeding 10^m, for m = 1, 2, ..., are 1, 29, 318, 3174, 31763, 317813, 3177179, 31774009, 317745099, 3177373819, ... . Apparently, the asymptotic density of this sequence exists and equals 0.3177... . - _Amiram Eldar_, Jun 24 2022
%H A083348 T. D. Noe, <a href="/A083348/b083348.txt">Table of n, a(n) for n = 1..1000</a>
%F A083348 A083345(a(n)) > A083346(a(n)).
%F A083348 A083345(A051674(n)) = A083346(A051674(n)).
%F A083348 A083345(A083347(n)) < A083346(A083347(n)).
%F A083348 A168036(a(n)) > 0. - _Reinhard Zumkeller_, May 22 2015
%t A083348 ad[n_] := Switch[n, 0 | 1, 0, _, If[PrimeQ[n], 1, Sum[Module[ {p, e}, {p, e} = pe; n e/p], {pe, FactorInteger[n]}]]];
%t A083348 Select[Range[1000], ad[#] > # &] (* _Jean-François Alcover_, May 04 2023 *)
%o A083348 (Haskell)
%o A083348 a083348 n = a083348_list !! (n-1)
%o A083348 a083348_list = filter ((> 0) . a168036) [1..]
%o A083348 -- _Reinhard Zumkeller_, May 22 2015, May 10 2011
%Y A083348 Cf. A003415, A072873, A051674, A083345, A083346, A083347, A168036, A369048 (characteristic function), A369049.
%Y A083348 Subsequence of A100717.
%K A083348 nonn
%O A083348 1,1
%A A083348 _Reinhard Zumkeller_, Apr 25 2003